This (partially) documents the usage of the verbose argument of the fitting functions, and more specifically of verbose["TRACE"] values.
Default is TRACE=FALSE (or 0) which is self-explanatory. TRACE=TRUE (or 1) shows values of outer-estimated parameters (and possibly fixed values of parameters that would be outer-estimated), some cryptic progress bar, and the attained value of the likelihood objective function (but when there inner-estimated dispersion parameters, the output is more difficult to describe concisely). Other values have effect may change in later versions without notice see Details).
If the fitted model includes a residual-dispersion mdoel, some tracing output for the latter may be confusingly intermingled with tracing output of the mean-response model. The Details are valid only for the mean-response model.
0<TRACE<1 only shows the cryptic progress bar.
TRACE=2 will further show information about the progress of Levenberg-Marquardt-like steps for linear-predictor coefficients.
TRACE=3 will further show information about the progress of distinct Levenberg-Marquardt-like steps random effects given fixed-effect coefficients.
TRACE=4 will further show cryptic information about which matrix computations are requested.
TRACE=5 will further report (through a call to the base trace function) the str(.) of the results of such matrix computations.
TRACE=6 will further pause between iterations of the reweighted least-squares algorithm, allowing a browser session to be called.